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Prescribed non positive scalar curvature on asymptotically hyperbolic manifolds with application to the Lichnerowicz equation (1909.05343v1)
Published 11 Sep 2019 in math.DG, gr-qc, and math.AP
Abstract: We study the prescribed scalar curvature problem, namely finding which function can be obtained as the scalar curvature of a metric in a given conformal class. We deal with the case of asymptotically hyperbolic manifolds and restrict ourselves to non positive prescribed scalar curvature. Following earlier results, we obtain a necessary and sufficient condition on the zero set of the prescribed scalar curvature so that the problem admits a (unique) solution.